What is the derivative of sqrt(9x+5) ?

The derivative of sqrt(9x+5) is 9/(2sqrt(9x+5))

What is the first derivative of sqrt(9x+5) ?

The first derivative of sqrt(9x+5) is 9/(2sqrt(9x+5))

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\frac{d}{d x} (9 x + 5)

\frac{9}{2 9 x + 5}

Solution steps

\frac{d}{d x} (9 x + 5)

Apply the chain rule:

\frac{1}{2 9 x + 5} \frac{d}{d x} (9 x + 5)

= \frac{1}{2 9 x + 5} \frac{d}{d x} (9 x + 5)

\frac{d}{d x} (9 x + 5) = 9

= \frac{1}{2 9 x + 5} \cdot 9

Simplify

\frac{1}{2 9 x + 5} \cdot 9 : \frac{9}{2 9 x + 5}

= \frac{9}{2 9 x + 5}

What is the derivative of sqrt(9x+5) ?
The derivative of sqrt(9x+5) is 9/(2sqrt(9x+5))
What is the first derivative of sqrt(9x+5) ?
The first derivative of sqrt(9x+5) is 9/(2sqrt(9x+5))